Parameter estimation of river incision models of soft sedimentary rocks – a case study on the Kamikita Coastal Plain, northeast Japan

Abstract. Understanding river incision model is crucial for predicting long-term landscape evolution. For the bedrock channel incision model (detachment-limited (DL) model: erosion rate E=KAmSn where A is drainage area, S is channel gradient), parameters (K, m, and n) can be estimated via slope-area analysis if E is known. Using 10Be denudation rate, previous studies globally compiled the parameter values for variable lithology. However, limited data availability for soft sedimentary rock restricts the applicability of global compilation. In addition, measuring the 10Be concentration in sedimentary rock is challenging in humid and tectonically active regions. To address this, slope-area analysis was conducted in the Kamikita Coastal Plain, Japan, where lithology (Miocene to Pleistocene sedimentary rocks) and uplift rate (∼ 0.2 mm yr−1 for the past 300 ka) are assumed to be uniform. River incision rates were derived approximately from widely distributed marine terraces (MIS 5e–11). For six target rivers, DL-like behaviour was confirmed in the limited areas located upstream of the alluvium distribution. The reference concavity m/n was 0.44 ± 0.10, typical for steady-state channels. Across the m/n range of 0.4–0.6, the exponent n consistently exhibited nonlinearity ranging between 1.14 to 1.34, which is consistent with the previous global compilations. This observed nonlinearity likely reflects transient landscape responses to past sea-level changes, which generated slope-break knickpoints at similar elevations. Finally, the estimated erosion coefficient K (10−5–10−6) agreed with the global relationship with unconfined compressive strength qu (K∝1/qu2), supporting the significant influences of bedrock lithology on K.